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It is here that we wade into conflict between Thomists and non-Thomists. Thomists uniquely deny the possibility of spiritual matter. Thus, we affirm that all pure spirits are pure forms, with only a composition of essence and existence. Thus, there cannot be multiple angels of the same species.
In the Sed Contra, St. Thomas brings his view forward in order to answer this question. He argues that in this union between form and matter, there always results "dimensive quantity," i.e., spatial extension. Now, when there is spatial extension, we have something that is three dimensional (i.e., a "body").